Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the degradation model such as blur kernel. In particular, we designed an algorithm based on the well-known Expectation-Minimization (EM) estimation method and diffusion models. Our method alternates between approximating the expected log-likelihood of the inverse problem using samples drawn from a diffusion model and a maximization step to estimate unknown model parameters. For the maximization step, we also introduce a novel blur kernel regularization based on a Plug \& Play denoiser. Diffusion models are long to run, thus we provide a fast version of our algorithm. Extensive experiments on blind image deblurring demonstrate the effectiveness of our method when compared to other state-of-the-art approaches.

翻译：利用扩散模型求解逆问题是当前一个新兴的研究领域。现有方法假定退化过程已知，并在恢复质量与多样性方面取得了令人瞩目的成果。本研究利用此类模型的高效性，联合估计恢复图像与退化模型（如模糊核）中的未知参数。具体而言，我们基于经典的期望-最大化（EM）估计方法设计了结合扩散模型的算法。该方法交替执行两步：利用扩散模型生成的样本近似逆问题的期望对数似然，以及通过最大化步骤估计未知模型参数。在最大化步骤中，我们还引入了一种基于即插即用去噪器的新型模糊核正则化方法。由于扩散模型运行耗时较长，我们进一步提出了算法的快速版本。在盲图像去模糊任务上的大量实验表明，与当前最先进方法相比，本方法具有显著有效性。